﻿418 
  Besearches 
  upon 
  Osmosis 
  and 
  Osmotic 
  Pressure. 
  

  

  In 
  the 
  case 
  of 
  small 
  leaks 
  we 
  have 
  the 
  osmotic 
  pressure 
  

   determined 
  by 
  equation 
  6 
  a, 
  § 
  3. 
  By 
  differentiating 
  with 
  

   regard 
  to 
  T 
  and 
  by 
  putting 
  

  

  VcWo 
  WW* 
  1 
  

  

  we 
  get 
  

  

  dfr 
  Q 
  _ 
  dir 
  Q 
  f 
  1 
  / 
  dt 
  _ 
  X 
  dS 
  \ 
  / 
  q 
  x 
  

  

  dl 
  " 
  dT 
  ~*~ 
  8\dX 
  ~$ 
  dl)- 
  ' 
  ' 
  * 
  w 
  

  

  7£ 
  

   Remembering 
  that 
  S, 
  3, 
  and 
  ^ 
  are 
  positive 
  quantities, 
  

  

  we 
  get 
  from 
  (8) 
  and 
  (9) 
  that 
  -^ 
  is 
  positive. 
  That 
  is 
  to 
  say, 
  

  

  that 
  the 
  quantities 
  -~f 
  k" 
  increase 
  with 
  the 
  temperature. 
  The 
  

  

  temperature 
  will 
  most 
  likely 
  to 
  some 
  extent 
  affect 
  both 
  quan- 
  

   tities, 
  but 
  at 
  all 
  events 
  we 
  must 
  assume 
  an. 
  increase 
  in 
  the 
  

   leak. 
  This 
  follows 
  from 
  the 
  behaviour 
  of 
  the 
  membrane 
  for 
  

   electric 
  currents. 
  Firstly, 
  we 
  have 
  seen 
  that 
  the 
  membrane 
  

   becomes 
  weaker 
  by 
  increasing 
  temperature 
  ; 
  and 
  secondly, 
  

   we 
  have 
  seen 
  that 
  even 
  if 
  the 
  membrane 
  keep 
  a 
  constant 
  

   mechanical 
  structure, 
  it 
  shoics 
  a 
  great 
  temperature 
  effect 
  

   which 
  is 
  best 
  explained 
  by 
  assuming 
  that 
  the 
  permea- 
  

   bility 
  of 
  the 
  membrane 
  for 
  the 
  ions 
  is 
  increased 
  by 
  tem- 
  

   perature. 
  And 
  the 
  increase 
  of 
  permeability 
  for 
  the 
  ions 
  must 
  

   correspond 
  to 
  an 
  increase 
  in 
  the 
  leak 
  of 
  solute. 
  

  

  As 
  long 
  as 
  we 
  cannot 
  determine 
  the 
  quantities 
  2 
  and 
  

  

  -tt^, 
  we 
  cannot 
  in 
  general 
  derive 
  the 
  temperature 
  effect 
  upon 
  

   ax. 
  

  

  osmotic 
  pressure 
  from 
  the 
  measured 
  quantity. 
  Then 
  we 
  only 
  

   get 
  the 
  relation 
  (8). 
  Just 
  as 
  by 
  the 
  determination 
  of 
  the 
  

   absolute 
  value 
  of 
  osmotic 
  pressure, 
  we 
  find 
  by 
  direct 
  mea- 
  

   surement 
  only 
  a 
  lower 
  limit 
  for 
  the 
  quantity 
  ( 
  -^ 
  J 
  , 
  and 
  

  

  consequently 
  the 
  way 
  of 
  proceeding 
  in 
  the 
  measurements 
  

   will 
  be 
  similar. 
  We 
  shall 
  have 
  for 
  a 
  certain 
  concentration 
  

   to 
  determine 
  a 
  ' 
  as 
  exactly 
  as 
  possible 
  in 
  each 
  case 
  ; 
  then 
  the 
  

   highest 
  value 
  would 
  give 
  the 
  value 
  nearest 
  to 
  the 
  temperature 
  

   coefficient 
  of 
  the 
  Osmotic 
  Pressure. 
  

  

  By 
  the 
  method 
  described 
  the 
  determination 
  of 
  a 
  ' 
  can 
  be 
  

   done 
  very 
  accurately. 
  The 
  accuracy 
  will 
  mainly 
  depend 
  

   upon 
  the 
  exactness 
  with 
  which 
  the 
  velocity 
  can 
  be 
  measured 
  

  

  and 
  upon 
  the 
  quantity 
  I 
  -=— 
  \ 
  . 
  

  

  In 
  general, 
  we 
  shall 
  have 
  the 
  greatest 
  accuracy 
  for 
  the 
  most 
  

  

  